Effects of finite-rate droplet evaporation on the ignition and propagation of premixed spherical spray flame

Abstract

Droplet evaporation might have great impact on fundamental spray combustion processes such as ignition, flame propagation, and extinction. In this study, we adopt and analyze a simplified model for spherical spray flame initiation and propagation in an overall fuel-rich or fuel-lean pre-mixture containing fuel droplet with finite-rate evaporation, fuel vapor, and air. We consider the limit of small droplets such that the medium can be considered as a continuum and adopt the sectional approach to model poly-disperse spray. Moreover, the thermal-diffusive model with constant density is employed and the spherical flame is assumed to propagate in a quasi-steady state. Under these assumptions, analytical correlations describing the change of flame propagation speed with flame radius are derived for the premixed spherical spray flame. The initial droplet load, vaporization Damköhler number, Lewis number, and ignition power are included in these correlations. Based on these correlations, spherical spray flame initiation and propagation are investigated with the emphasis on assessing the impact of droplet evaporation at different Lewis numbers. It is found that the spray flame propagation speed, Markstein length, and minimum ignition power are affected in different ways by the initial droplet load and vaporization Damköhler number and that the influence depends on Lewis number. Moreover, the influence of droplet evaporation on the fuel-lean case is greatly different from that on the fuel-rich case. This is mainly due to the facts that the fuel-rich spherical spray flame is affected by droplet evaporation only through latent heat of vaporization absorbed in the pre-flame and post-flame zones; while the fuel-lean spherical spray flame is affected by droplet evaporation through (1) latent heat of vaporization absorbed in the pre-flame and post-flame zones and (2) change in local effective equivalence ratio. For hydrocarbon fuels with large Lewis number, the lean spray flame is much more difficult to be ignited compare to the equivalent purely gaseous flame.